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Research in Brief Center for Law & Human Behavior The University of Texas at El Paso Game Theory & Adversarial Reasoning Modeling Decisions as Games . 6 December 1, 2016 Research in Brief DHS SYMPOSIUM SERIES NO DHS SYMPOSIUMSERIES Center for Law & Human Behavior The University of Texas at El Paso 500 West University Avenue Prospect Hall, Room 226 El Paso, Texas 79968 Tel: (915) 747-5920 Email: [email protected] Website: http://clhb.utep.edu Follow us on Twitter @1CLHB The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security. This symposium is supported by the U.S. Department of Homeland Security, Science and Technology, Office of University Programs under Grant Award Number DHS-14-ST-061-COE-00. Abstract information, time and equilibrium. Game theory has been applied to many domains, such as biology and population evolution, Many decisions in homeland security and transportation, computer network, political law enforcement are fundamentally about sciences, health care, business and supply adversarial interactions between multiple chain, insurance, cybersecurity, and agents with opposing interests. We personal life and thinking. Game theory provide a broad overview of recent has also been studied extensively in research that seeks to develop better data analysis and modeling techniques to homeland security. provide decision support for complex One of the most common uses of game security decisions, such as how to optimally theory in homeland security is to optimize allocate security resources. We provide the allocation of security resources, such as simple examples to illustrate the basic deployments of officers, vehicle patrols, K9 concepts, and then discuss a number of units, or the use of screening methods examples of different applications of these during inspections (Tambe, 2011). The methods to a wide variety of problems in basic problem in these cases is that there the context of homeland security and law are limited resources that must be used as enforcement. We also highlight some of effectively as possible to increase security. our ongoing research to improve the For example, a limited number of units may fundamental methods to make them be assigned to patrol a large number of scalable and broadly applicable to new possible locations that may be the target of types of problems. Finally, we provide examples of how close collaboration with attacks or other illegal activity. end users and decision makers has led to One of the important aspects of allocating useful deployments of adversarial resources effectively in adversarial domains reasoning to solve real-world problems is unpredictability. Since we are facing an leading to increased effectiveness. intelligent, adaptive adversary who can learn about the security policy, it is not Introduction sufficient in most cases to use a static, predictable deployment strategy for Game theory is a branch of applied allocating security resources. Instead, we mathematics that is used in the social focus on finding optimal randomized sciences, most notably in economics. policies that keep the attacker guessing, Game theory is also used in biology, limiting the effectiveness of surveillance engineering, political science, international and increasing deterrence, while relations, computer science, and maintaining protection of the most critical philosophy. Game theory attempts to assets. mathematically capture behavior in strategic situations where an individual's It is also possible to model both strategic success in making choices depends on the attackers and random events (e.g., natural choices of others. The key components of a disasters or accidents) using this approach. game include: players, options/moves, For example, using attacker-defender sequence of moves, objectives/payoffs, games, Zhuang and Bier (2007) apply game theory to identify the attacker’s and ARMOR-K9 uses game theory to create defender’s equilibrium strategies, in the randomized schedules for the K9 patrols. resource allocation game to counter Again, optimizing the need for terrorism and natural disasters. Zhuang unpredictable schedules while taking into and Bier (2007) balance resource allocation account risk information about the between terrorism and natural disasters. different terminals and time periods. Instead of a discrete choice, this work considers the attacker’s choice using a The ARMOR system has been in continuous continuous level of effort. It is found that use at LAX since 2007, and has been viewed when the defensive investment increases, as a highly successful program in improving an attacker can either increase his level of the security of the airport. effort to compensate for the reduced probability or decrease his level since the IRIS: FAMS Scheduling attack becomes less profitable. Following the success of ARMOR, our team worked with the Federal Air Marshals ARMOR: LAX Security Service (FAMS) to develop a scheduling One of the first uses of game theory in a system for randomizing the flight major deployed decision support system scheduling for the air marshals using a for homeland security was the ARMOR similar game-theoretic approach system developed for the Los Angeles, CA (Kiekintveld, 2008). This system generates (LAX) airport (Pita, 2008). The ARMOR unpredictable flight schedules for a system uses game theory to find optimal specified number of FAMS teams. The schedules for two resource allocation system, again, takes into account risk problems at the airport. The first is the evaluations of the flights and airports to vehicle checkpoints problem. Checkpoints determine the optimal schedule. In are used to screen vehicles entering the addition, this system must account for a terminal areas of the airport. However, large number of complex scheduling there are several potential access points. constraints to generate a feasible schedule There are insufficient resources to man for the air marshals to fly. The complexity checkpoints on all inbound routes at all of the scheduling problem in combination times, so the checkpoints must be allocated with the scale of the resource allocation strategically. ARMOR-checkpoints utilizes problem, due to the massive number of game theory to randomly assign the possible flights and large number of air checkpoints, balancing the importance of marshals, required new breakthroughs in the different routes and terminals with the computational methods for security games need to be unpredictable. to be able to develop the software system, IRIS. The second problem is the K9 scheduling problem. There are a limited number of K9 After extensive evaluation by the research units available to patrol the LAX terminals, team and internal evaluation by FAMS, the so there is a similar problem with deciding IRIS system was initially deployed for where and when to schedule K9 patrols in scheduling international flights in 2009, the terminals using the limited resource. and use of the system has been expanded since that time. Ongoing research stage game is considered. In the context of continues to provide more advanced game terrorism, the attacker usually learns the models and software tools to support defender’s private information. Xu and scheduling (Tsai, 2009). Zhuang (2016) analyze the strategic interactions of the attacker’s learning and Modeling Secrecy and Deception the defender’s counter-learning. They find Different from natural disasters where the that the attacker’s best responses and the resource allocation is usually disclosed, in defender’s equilibrium deception and terrorism, attackers are adaptive, and the defense strategies are significantly investments are not always disclosed to the impacted by the attacker’s cost of learning. public. It is important and challenging for the government to understand when and Multi-Period Attacker-Defender how such investment should be disclosed. Games It is important and challenging to Zhuang and Bier (2010) study the understand how to defeat terrorist threats conditions when a defender should choose over time. We need to assess the terrorist’s secrecy or deception about the investments capacity to attack over time. Hausken and in a homeland-security context. In games Zhuang (2011) study the timing of attacks with no private defender information, and the terrorist’s option of stockpiling truthful disclosure is preferred to secrecy attack resources using a two-period game, and deception as long as the cost of where the attacker chooses whether or not implementing truthful disclosure is lower to stockpile resources from the first to the than the costs of secrecy and deception. In second period. Besides the terrorist’s games with private defender information, capacity to attack over time, how the secrecy and deception may be strictly attacks can be deterred as time passes is preferred by the defender at equilibrium, in another issue which is studied in Hausken order to mimic other types of defenders, and Zhuang (2012). Hausken and Zhuang even if the cost of implementing truthful (2012) develop a model to study the timing disclosure is lower than the costs of secrecy and deterrence of terrorist attacks in a T- and deception (Zhuang and Bier, 2010). period game where a two-stage game (the Zhuang et al. (2010) model defender defender moves first and the attacker secrecy and deception in a multiple-period moves second) is analyzed in each period. attacker-defender game.
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